Hat Guessing Game: Hint

You are probably thinking that the best strategy can work only in 50% of the cases. The three people could designate one of them as the official guesser, who will say "My hat is red" while the two other pass. The guesser will be right half of the time.

Well, think again. There is a much better strategy. Consider the fact that if a person says "red" they will be right 50% of the time. The same with "blue." But when they say "pass," they are always right! Except, of course, when the two others pass as well. So you can see that there is a hint of a strategy that averages the three odds, 50%, 50%, and 100%, to something higher than 50%. You just have to cleverly avoid collisions between competing guesses.